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A000908 Atom-rooted polyenoids with n edges with symmetry class C_s. 0
0, 0, 1, 4, 14, 47, 164, 565, 1982, 6977, 24850, 89082, 321855, 1169853, 4276923, 15713799, 57998270, 214934984, 799473752, 2983682702, 11169374372, 41929478873, 157807392886, 595340271682, 2250901007539, 8527699269192, 32369066434276 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..26.

S. J. Cyvin, J. Brunvoll, E. Brendsdal, B. N. Cyvin and E. K. Lloyd, Enumeration of polyene hydrocarbons: a complete mathematical solution, J. Chem. Inf. Comput. Sci., 35 (1995) 743-751.

S. J. Cyvin, J. Brunvoll, E. Brendsdal, B. N. Cyvin and E. K. Lloyd, Enumeration of polyene hydrocarbons: a complete mathematical solution, J. Chem. Inf. Comput. Sci., 35 (1995) 743-751. [Annotated scanned copy]

FORMULA

a(n) = A003446(n) - u((n-3)/6) - (u(n/3) + u((n-3)/6))/2 - (u(n/2) + (u((n+1)/2) - u((n-3)/6))) for n > 3 where u(n) = binomial(2*n, n)/(n+1) if n is an integer and 0 otherwise. - Sean A. Irvine, Oct 05 2015

CROSSREFS

Cf. A000912, A000913, A000935, A000936, A000941, A000942, A000947, A000948, A000953, A003446, A063786.

Sequence in context: A320404 A137284 A228178 * A121095 A264816 A332610

Adjacent sequences:  A000905 A000906 A000907 * A000909 A000910 A000911

KEYWORD

nonn

AUTHOR

E. K. Lloyd (E.K.Lloyd(AT)soton.ac.uk)

EXTENSIONS

More terms from Sean A. Irvine, Oct 05 2015

STATUS

approved

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Last modified January 22 02:46 EST 2022. Contains 350481 sequences. (Running on oeis4.)